Problem: Simplify the following expression: $a = \dfrac{z^2 - 7z - 30}{z + 3} $
First factor the polynomial in the numerator. $ z^2 - 7z - 30 = (z + 3)(z - 10) $ So we can rewrite the expression as: $a = \dfrac{(z + 3)(z - 10)}{z + 3} $ We can divide the numerator and denominator by $(z + 3)$ on condition that $z \neq -3$ Therefore $a = z - 10; z \neq -3$